21-Mat-B6 Ceramic Materials · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
The driving force is purely thermodynamic: the volume (chemical) free-energy difference $\Delta G_v$ between austenite and the (metastable) martensite phase, made available by undercooling austenite well below its equilibrium $T_0$ temperature (the temperature at which austenite and martensite of the same composition would have equal free energy). Because the transformation is diffusionless and must also do MECHANICAL work against the elastic and plastic strain-energy resistance of the surrounding, already-transformed material (the shape change is large: martensite forms as thin, strained plates/laths that must accommodate a shear plus a volume expansion within a still-rigid austenite matrix), a substantial undercooling below $T_0$ — down to $M_s$ — is required before $\Delta G_v$ is large enough to overcome this strain-energy penalty and drive the transformation. $M_s$ is therefore the temperature at which the growing free-energy driving force first exceeds the (composition-dependent) strain-energy resistance.
Martensite forms by a coordinated, diffusionless, homogeneous shear (shuffle) mechanism: atoms move cooperatively, each by less than one interatomic spacing relative to its neighbours, preserving the same nearest-neighbour relationships (no long-range diffusion, no compositional change from the parent austenite) while collectively converting the FCC austenite lattice into a body-centred-tetragonal (BCT) martensite lattice. The transformation propagates athermally, at speeds approaching the speed of sound in the lattice, along specific crystallographic habit planes with an invariant-plane strain (a combination of shear plus a small volume-expansion component normal to the habit plane), nucleating and growing as thin lenticular plates or laths rather than by any interface migrating diffusionally. Carbon, which was in interstitial solid solution in FCC austenite, has no time to partition or diffuse out during this shear and is trapped in the smaller, more anisotropic octahedral sites of the BCT lattice, which is exactly what generates the large tetragonal distortion (c/a ratio increasing with carbon content) responsible for martensite's hardness. This mechanism is NOT unique to steel: any diffusionless, shear-dominated, shape-memory-type transformation between two crystal structures is generically called "martensitic," and the term is used equally for non-ferrous alloys (Ti alloys, Cu-based and Ni-Ti shape-memory alloys, Co alloys), and even for some ceramics (e.g. the tetragonal-to-monoclinic transformation in zirconia) — steel's interstitial-carbon-driven hardening is simply the best-known and most technologically important example of the family.
Trapped interstitial carbon is the dominant strengthening term in martensite, and its effect intensifies directly with concentration for two compounding reasons. First, each interstitial carbon atom that occupies the (undersized, asymmetric) octahedral site of the BCT lattice produces a local tetragonal distortion; as carbon content rises, the lattice's OWN average tetragonality ($c/a$ ratio) increases systematically, and this lattice distortion is exactly what most strongly resists dislocation motion (a long-range, strong interstitial-solute strengthening effect, well above ordinary solid-solution strengthening in a substitutional system). Second, higher carbon content also increases the density of the dislocations/internal twins generated by the shear transformation itself, adding a compounding substructure-strengthening contribution. Both mechanisms scale up together with wt%C, which is why measured as-quenched martensite hardness rises steeply and almost linearly with carbon content up to about 0.6–0.7 wt% C (beyond which retained austenite and diminishing returns in tetragonality flatten the curve).
